Rhythmic Stability

Mitch, Ronan, Bokum

Basic Expectancy

0 A 2A 3A 4A 5A

0

time interval B

Bas

ic e

xpe

ctan

cy

E

(A,B

)b

A_2

Basic Expectancy Model

nn

R prefb T

BARR

B

AGAUSSBAE

,,2,1,2

1,,

1

,,),(

2),(),(),,( xSRDeSRCSRxGAUSS

• C(R,S) scales the height

• D(R,S) scales the width

Our Implementation

)/1,max(),( RRSRD

),S,lognormal()/1,max(),( 3 RRSRC

2

102log

2

1exp

2

1),,(lognormal SS

Paulus and Klapuri 2002

Scale height by reciprocal integer ratio

Scale width exponentially and weight by likelihood of tempo

Complex Expectancy

• All preceding durations contribute to future expectancy.

e q q e

temporal pattern complex expectancy

0 2 4 6 8 10 12

basic expectanciesimplied intervals

timenowpast future

C

Computing Stability of Segment

• For each onset compute stability of each duration pair it divides.

• Total stability is geometric mean of onset stabilities:– Mean(a)=product(a)^(1/N), where N is the

length of vector a.

Results

0 A 2A 3A 4A 5A

0

time interval B

Ba

sic

ex

pe

cta

nc

y E

(A

,B)

b

A_2